My linux counterparts use git + puppet to manage their linux systems. They have asked me to look into using DSC with git (easy enough) but they want me to install puppet as the push method. I feel like that takes away part of what DSC can do.

So if I install puppet on a windows box, then push DSC from our git repo via puppet, interesting place. I think this is likely going to add unneeded complexity as then I have to manage puppet manifests/profiles etc.

In WMF 5.0, DSC integrates very well with other config management tools such as Puppet. In that case, you wouldn't be writing DSC configurations at all, but your Puppet configurations (whatever they're called) would be able to make use of DSC resources via the new Invoke-DscResource command. I'm not sure if that's the scenario you're describing or not, though, and WMF 5.0 isn't production yet.

If you're talking about having Puppet just act as a deployment tool for DSC configs (where Puppet's agent would be compiling MOFs from PowerShell code, and running Start-DscConfiguration), that seems a bit weird to me, but it could still work. We do something similar with Octopus Deploy.

Maybe a bit off topic, but at Ignite there was a presentation about GIT webhooks and Azure Automation, which can act as your trigger mechanism for deployment, updating and CI builds. Basically, you link a GIT event to a Runbook. This can be targeted to Azure or local server(s). It's seriously mouth watering stuff.